Write an equation of the line that passes through the points $( - 1,1.6 )$ and $( - 3 , - 4.4 )$ . Write the equation in general form.
A) $x - 3 y - 4.6 = 0$
B) $3 x + y + 5.8 = 0$
C) $- 3 x + y + 5.8 = 0$
D) $- 3 x + y - 4.6 = 0$
E) $x + 3 y - 4.6 = 0$

Question

Quizplus · Accepted Answer

The equation can be found using the slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. First, we need to find the slope of the line using the two points:
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4.4 - 1.6}{-3 - (-1)} = \frac{-6}{-2} = 3$$
Now we can use the point-slope form of the equation, substituting one of our given points:
$$y - y_1 = m(x - x_1)$$
$$y - 1.6 = 3(x + 1)$$
Simplifying, we get:
$$y = 3x + 4.4$$
To put it in general form, we can move the constant term to the other side:
$$-3x + y - 4.4 = 0$$
Which matches choice D.

Write an Equation of the Line That Passes Through the Points